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In algebra, Can a Constant Have a Coefficient?

Coefficient

A coefficient can be defined as integer which is multiplied with the variable of a single term or the terms of a polynomial. A coefficient is a number, but sometimes it may be a letter in an expression. Let us take an example. In the expression ax2 + bx + c, x is the variable and ‘a’ and ‘b ‘are the coefficients.

What is a Coefficient?

A coefficient is the number or quantity placed with a variable. It is an integer which is multiplied by the variable placed next to it. The variables which do not have a number with them are taken as 1 as their coefficient. For example, 3 is the coefficient in the expression 3x and in the expression x2 + 3, 1 is assumed as the coefficient of x2. Thus, a coefficient is said to be a multiplicative factor in a polynomial, a series, or any expression. It is a number. Now, let us observe the following expression which shows that 5 is the coefficient of x2 and 8 is the coefficient of y.

How to find a coefficient?

The most important thing to be remembered while finding a coefficient is that it always comes with a variable. Let us take the expression 5×2 + 2y _ 7. Here there are three terms: 5×2, 2y, 7. In 5×2, x is the variable and the coefficient is 5. In 2y, y is the variable and the coefficient is 7. In the last term, 7 is the constant.

Numerical coefficient

A numerical coefficient is a number which is a multiplier of the variables in a term. In the example 3mn, 3 is the numerical coefficient. Numerical coefficient is used for the constant multipliers of variable. In the example 4xy, the numerical coefficient of xy is 4.

Characteristics of a coefficient

A coefficient come in the form of positive or negative,real or imaginary, decimals or fractions. In the example 9.3x, 9.3 is the coefficient of the variable x, and in -5z,-5 is the coefficient.

Key points

  • A coefficient always comes with a variable.
  • 1 is the coefficient of a variable without a number.
  • The value of a variable varies depending on the question and situation.
  • The value of a constant is always constant because its value is fixed and can never change.

What is a constant?

Constant is defined as that entity whose value is always fixed though its usage varies.

The values do not change even when there is a change in expression.

Constants comes in the form of numerical value like a natural number, whole number, real number, integer or decimal number.

Variable is that entity whose value varies depending on the change in its usage.

Some real-life examples are:

  • The shoe size of a 40-year-old man is constant and does not change.
  • The number of fingers in our hands are always constant and does not change.
  • The number of eyes is always constant.

What are variables and constant in an algebraic expression?

An algebraic can be defined as a mathematical expression which consists of variables, constants, coefficients and mathematical operators.

Given below is an example to understand it better

Variables are denoted by letters or symbols and constants are numbers.

Now coming to the question whether in an algebraic expression, a constant can have a coefficient or not.

In an equation in a variable x, any part of the equation which is independent of x is a constant term.

Therefore, it can be said that the coefficients of algebraic expressions are constants.

But it is to be noted that some constants are not coefficients and ‘variable coefficients” occurs in some cases.

A polynomial is a sum of coefficients times powers of the variable. Thus, in the polynomial, 3×2 + 4x + 5, it has three coefficients, namely, 3, 4 and 5.

Also, the sum and difference of two polynomials is a polynomial which means that we have to take numbers which are polynomials, such that the difference of 3×2 + 4x + 5 and 3×2 + 4x + 2, is 3.

Now when 3 is a polynomial, and a polynomial is a sum of coefficients times powers of the variable, then the constant 3 is a coefficient which is 3 times x0.

Thus, constants have in themselves as coefficients.

Learn More: Algebraic Expressions From Class 7 Maths

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